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A cluster of results on amplituhedron tiles 关于振子面砖的一组成果
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-09-11 DOI: 10.1007/s11005-024-01854-4
Chaim Even-Zohar, Tsviqa Lakrec, Matteo Parisi, Melissa Sherman-Bennett, Ran Tessler, Lauren Williams
{"title":"A cluster of results on amplituhedron tiles","authors":"Chaim Even-Zohar,&nbsp;Tsviqa Lakrec,&nbsp;Matteo Parisi,&nbsp;Melissa Sherman-Bennett,&nbsp;Ran Tessler,&nbsp;Lauren Williams","doi":"10.1007/s11005-024-01854-4","DOIUrl":"10.1007/s11005-024-01854-4","url":null,"abstract":"<div><p>The amplituhedron is a mathematical object which was introduced to provide a geometric origin of scattering amplitudes in <span>(mathcal {N}=4)</span> super Yang–Mills theory. It generalizes <i>cyclic polytopes</i> and the <i>positive Grassmannian</i> and has a very rich combinatorics with connections to cluster algebras. In this article, we provide a series of results about tiles and tilings of the <span>(m=4)</span> amplituhedron. Firstly, we provide a full characterization of facets of BCFW tiles in terms of cluster variables for <span>(text{ Gr}_{4,n})</span>. Secondly, we exhibit a tiling of the <span>(m=4)</span> amplituhedron which involves a tile which does not come from the BCFW recurrence—the <i>spurion</i> tile, which also satisfies all cluster properties. Finally, strengthening the connection with cluster algebras, we show that each standard BCFW tile is the positive part of a cluster variety, which allows us to compute the canonical form of each such tile explicitly in terms of cluster variables for <span>(text{ Gr}_{4,n})</span>. This paper is a companion to our previous paper “Cluster algebras and tilings for the <span>(m=4)</span> amplituhedron.”</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01854-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On an inequality of Lin, Kim and Hsieh and strong subadditivity 论林、金、谢的不等式和强次二项性
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-09-09 DOI: 10.1007/s11005-024-01857-1
Eric A. Carlen, Michael P. Loss
{"title":"On an inequality of Lin, Kim and Hsieh and strong subadditivity","authors":"Eric A. Carlen,&nbsp;Michael P. Loss","doi":"10.1007/s11005-024-01857-1","DOIUrl":"10.1007/s11005-024-01857-1","url":null,"abstract":"<div><p>We give an elementary proof of an inequality of Lin, Kim and Hsieh that implies strong subadditivity of the von Neumann entropy.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01857-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A general construction of family algebraic structures 族代数结构的一般构造
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-09-09 DOI: 10.1007/s11005-024-01851-7
Loïc Foissy, Dominique Manchon, Yuanyuan Zhang
{"title":"A general construction of family algebraic structures","authors":"Loïc Foissy,&nbsp;Dominique Manchon,&nbsp;Yuanyuan Zhang","doi":"10.1007/s11005-024-01851-7","DOIUrl":"10.1007/s11005-024-01851-7","url":null,"abstract":"<div><p>We give a general account of family algebras over a finitely presented linear operad. In a family algebra, each operation of arity <i>n</i> is replaced by a family of operations indexed by \u0000<span>(Omega ^n)</span>, where \u0000<span>(Omega )</span> is a set of parameters. We show that the operad, together with its presentation, naturally defines an algebraic structure on the set of parameters, which in turn is used in the description of the family version of the relations between operations. The examples of dendriform and duplicial family algebras (hence with two parameters) and operads are treated in detail, as well as the pre-Lie family case. Finally, free one-parameter duplicial family algebras are described, together with the extended duplicial semigroup structure on the set of parameters.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Commutative Poisson algebras from deformations of noncommutative algebras 来自非交换代数变形的交换泊松代数
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-08-29 DOI: 10.1007/s11005-024-01855-3
Alexander V. Mikhailov, Pol Vanhaecke
{"title":"Commutative Poisson algebras from deformations of noncommutative algebras","authors":"Alexander V. Mikhailov,&nbsp;Pol Vanhaecke","doi":"10.1007/s11005-024-01855-3","DOIUrl":"10.1007/s11005-024-01855-3","url":null,"abstract":"<div><p>It is well-known that a formal deformation of a commutative algebra <span>(mathcal {A})</span> leads to a Poisson bracket on <span>(mathcal {A})</span> and that the classical limit of a derivation on the deformation leads to a derivation on <span>(mathcal {A})</span>, which is Hamiltonian with respect to the Poisson bracket. In this paper we present a generalization of it for formal deformations of an arbitrary noncommutative algebra <span>(mathcal {A})</span>. The deformation leads in this case to a Poisson algebra structure on <span>(Pi (mathcal {A}){:}{=}Z(mathcal {A})times (mathcal {A}/Z(mathcal {A})))</span> and to the structure of a <span>(Pi (mathcal {A}))</span>-Poisson module on <span>(mathcal {A})</span>. The limiting derivations are then still derivations of <span>(mathcal {A})</span>, but with the Hamiltonian belong to <span>(Pi (mathcal {A}))</span>, rather than to <span>(mathcal {A})</span>. We illustrate our construction with several cases of formal deformations, coming from known quantum algebras, such as the ones associated with the nonabelian Volterra chains, Kontsevich integrable map, the quantum plane and the quantized Grassmann algebra.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01855-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence and asymptotic behavior of nontrivial p-k-convex radial solutions for p-k-Hessian equations p-k-Hessian 方程的非rivial p-k-convex 径向解的存在性和渐近行为
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-08-23 DOI: 10.1007/s11005-024-01858-0
Meiqiang Feng, Yichen Lu
{"title":"Existence and asymptotic behavior of nontrivial p-k-convex radial solutions for p-k-Hessian equations","authors":"Meiqiang Feng,&nbsp;Yichen Lu","doi":"10.1007/s11005-024-01858-0","DOIUrl":"10.1007/s11005-024-01858-0","url":null,"abstract":"<div><p>We study, via the eigenvalue theory of completely continuous operators, the existence and asymptotic behavior of nontrivial <i>p</i>-<i>k</i>-convex radial solutions for a <i>p</i>-<i>k</i>-Hessian equation. This is probably the first time that <i>p</i>-<i>k</i>-Hessian equations have been studied by employing this technique. Several new nonexistence conclusions are also derived in this paper.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mourre theory and spectral analysis of energy-momentum operators in relativistic quantum field theory 相对论量子场论中的莫尔理论和能动算子谱分析
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-08-22 DOI: 10.1007/s11005-024-01859-z
Janik Kruse
{"title":"Mourre theory and spectral analysis of energy-momentum operators in relativistic quantum field theory","authors":"Janik Kruse","doi":"10.1007/s11005-024-01859-z","DOIUrl":"10.1007/s11005-024-01859-z","url":null,"abstract":"<div><p>A central task of theoretical physics is to analyse spectral properties of quantum mechanical observables. In this endeavour, Mourre’s conjugate operator method emerged as an effective tool in the spectral theory of Schrödinger operators. This paper introduces a novel class of examples from relativistic quantum field theory that are amenable to Mourre’s method. By assuming Lorentz covariance and the spectrum condition, we derive a limiting absorption principle for the energy-momentum operators and provide new proofs of the absolute continuity of the energy-momentum spectra. Moreover, under the assumption of dilation covariance, we show that the spectrum of the relativistic mass operator is purely absolutely continuous in <span>((0,infty ))</span>.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01859-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Support of the free measure for quantum field on fractal space-time 分形时空中量子场自由度的支持
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-08-13 DOI: 10.1007/s11005-024-01853-5
Tianjia Ni
{"title":"Support of the free measure for quantum field on fractal space-time","authors":"Tianjia Ni","doi":"10.1007/s11005-024-01853-5","DOIUrl":"10.1007/s11005-024-01853-5","url":null,"abstract":"<div><p>In constructive quantum theory, the free field is constructed based on a Gaussian measure on the space of tempered distributions. We generalize the classic results about support property of the Gaussian measure from Euclidean space-time to fractal space-time <span>(mathbb {R}times F)</span>. More precisely, we show that the set <span>((I-Delta _F)^{(d_s-1)/4+alpha }(1+| x| ^2)^{(d_H+1)/4+beta }L^2(mathbb {R}times F))</span> is of the Gaussian measure one if <span>(alpha &gt;0)</span> and <span>(beta &gt;0)</span>, while the set is of the Gaussian measure zero if <span>(alpha &gt;0)</span> and <span>(beta &lt;0)</span>. Here, <span>(Delta _F)</span> is the Laplacian on the underlying fractal space <i>F</i>, <span>(d_s)</span> is the spectral dimension of <span>(Delta _F)</span>, and <span>(d_H)</span> is the Hausdorff dimension of <i>F</i>.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Jucys–Murphy basis and semisimplicity criteria for the q-Brauer algebra q-Brauer 代数的 Jucys-Murphy 基和半简性标准
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-08-12 DOI: 10.1007/s11005-024-01850-8
Hebing Rui, Mei Si, Linliang Song
{"title":"The Jucys–Murphy basis and semisimplicity criteria for the q-Brauer algebra","authors":"Hebing Rui,&nbsp;Mei Si,&nbsp;Linliang Song","doi":"10.1007/s11005-024-01850-8","DOIUrl":"10.1007/s11005-024-01850-8","url":null,"abstract":"<div><p>We construct the Jucys–Murphy elements and the Jucys–Murphy basis for the <i>q</i>-Brauer algebra in the sense of Mathas. We also give a necessary and sufficient condition for the <i>q</i>-Brauer algebra being (split) semisimple over an arbitrary field.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Correction to: Ruminations on matrix convexity and the strong subadditivity of quantum entropy 更正：关于矩阵凸性和量子熵强次可加性的遐想
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-08-08 DOI: 10.1007/s11005-024-01849-1
Michael Aizenman, Giorgio Cipolloni
{"title":"Correction to: Ruminations on matrix convexity and the strong subadditivity of quantum entropy","authors":"Michael Aizenman,&nbsp;Giorgio Cipolloni","doi":"10.1007/s11005-024-01849-1","DOIUrl":"10.1007/s11005-024-01849-1","url":null,"abstract":"","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141929431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized double affine Hecke algebra for double torus 双环的广义双仿射赫克代数
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-08-07 DOI: 10.1007/s11005-024-01848-2
Kazuhiro Hikami
{"title":"Generalized double affine Hecke algebra for double torus","authors":"Kazuhiro Hikami","doi":"10.1007/s11005-024-01848-2","DOIUrl":"10.1007/s11005-024-01848-2","url":null,"abstract":"<div><p>We propose a generalization of the double affine Hecke algebra of type-<span>(C^vee C_1)</span> at specific parameters by introducing a “Heegaard dual” of the Hecke operators. Shown is a relationship with the skein algebra on double torus. We give automorphisms of the algebra associated with the Dehn twists on the double torus.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01848-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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